Unified Lyapunov-Based Integral Nonsingular Fast Terminal Sliding Mode Control for Nonlinear Systems with Quantitative Performance Evaluation

Abstract

This paper presents a Unified Lyapunov-Based Integral Nonsingular Fast Terminal Sliding Mode Control (ULI-NFTSMC) framework for tracking nonlinear systems subject to parametric uncertainties and bounded matched disturbances. The proposed controller incorporates proportional and integral error dynamics into a nonsingular fast terminal sliding surface and employs a bounded integral-state mechanism to limit integral accumulation during large transients and actuator saturation. The formulation is developed using a matched-uncertainty representation of the nonlinear system, and a Lyapunov-based analysis establishes a sufficient switching-gain condition for finite-time reachability of the proposed sliding variable. The controller design combines integral error augmentation with nonsingular fast terminal dynamics while avoiding the singularity associated with conventional terminal sliding-mode formulations. The proposed approach is evaluated using a nonlinear coupled twin-tank liquid-level process under nominal operating conditions and under parametric uncertainty with an external disturbance. Tracking performance and control characteristics are assessed using integral absolute error (IAE), integral squared error (ISE), control smoothness index (CSI), control requirement coefficient (CRC), and total normalized control-effort index (TECI). The simulation study demonstrates the applicability of the proposed ULI-NFTSMC framework to nonlinear uncertain process-control systems and provides quantitative measures of tracking accuracy, control-signal variation, and control effort.